按方法、领域与证据探索科学。

NARDL Model

The NARDL model, introduced by Shin, Yu and Greenwood-Nimmo in 2014, extends the ARDL framework to capture asymmetric long-run and short-run relationships, testing whether positive and negative changes in a regressor affect the dependent variable differently.

econometrics

Negative Binomial Regression

Negative Binomial Regression is a generalized linear model for count outcomes that extends Poisson regression to handle overdispersion, where the variance of the counts exceeds their mean. Developed in the GLM tradition and treated in depth by Hilbe (2011), it adds a dispersion parameter so that inference stays valid w

survival

Nelson-Aalen Estimator

The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function from right-censored time-to-event data. Developed by Wayne Nelson for reliability hazard plotting in 1972 and placed on a rigorous counting-process foundation by Odd Aalen in 1978, it accumulates the ratio of observed events to t

statistics

Nemenyi Test

The Nemenyi test is a nonparametric post-hoc multiple comparison procedure introduced by Peter Nemenyi in his 1963 Princeton doctoral thesis. It is applied after a significant Friedman test to identify which specific pairs of conditions differ from each other in a repeated-measures or blocked design.

econometrics

Nested Logit

The Nested Logit model is a discrete choice framework that groups mutually exclusive alternatives into hierarchical nests, allowing correlated unobserved utilities within each nest while maintaining independence across nests. Introduced formally by Ben-Akiva and Lerman (1985) and grounded in McFadden's Generalized Extr

forensics

Network Analysis of Case Law

Network analysis of case law applies graph-theoretic and network science methods to study the structure and dynamics of legal precedent systems. Developed systematically by James Fowler and colleagues in 2011, this method treats legal citations as directed edges in a network where nodes represent court decisions and ed

econometrics

Network Econometrics

Network econometrics estimates how individuals' outcomes are causally shaped by the behaviour and characteristics of their social-network neighbours. Formalised by Bramoullé, Djebbari, and Fortin (2009), the framework embeds a row-normalised adjacency matrix into a linear regression, separating endogenous peer effects

bioinformatics

Network-based gene set enrichment analysis

Network-based gene set enrichment analysis (network GSEA) extends classical GSEA by incorporating biological interaction networks — such as protein-protein interaction (PPI) or co-expression graphs — into the enrichment test. Instead of treating each gene independently, the method propagates differential expression sig

spatial analysis

Network-Based Spatial Analysis

Network-based spatial analysis (NBSA) analyzes the distribution and interaction of spatial phenomena constrained to a network structure — such as roads, railways, or rivers — using network distance rather than straight-line (Euclidean) distance. It is the appropriate framework whenever movement, proximity, or risk is g

econometrics

Newey-West HAC

Newey-West HAC standard errors, introduced by Whitney Newey and Kenneth West in 1987, provide a covariance matrix estimator for OLS regression that remains valid under both heteroskedasticity and serial autocorrelation of unknown form. They are the standard tool for correcting inference in time-series and panel regress

bayesian

No-U-Turn Sampler

The No-U-Turn Sampler (NUTS) is a self-tuning Markov chain Monte Carlo algorithm introduced by Hoffman and Gelman (2014) that extends Hamiltonian Monte Carlo (HMC) by automatically determining the optimal number of leapfrog steps, eliminating the most sensitive manual tuning parameter. NUTS is the default sampler in St

econometrics

Nonlinear ADF Unit Root Test

The Nonlinear ADF unit root test, most prominently operationalized by Kapetanios, Shin, and Snell (2003), extends the classical Augmented Dickey-Fuller test to detect mean reversion that occurs via an Exponential Smooth Transition Autoregressive (ESTAR) process. It tests the null of a unit root against a nonlinear stat

econometrics

Nonlinear AR Model

The Nonlinear AR model extends the classical autoregressive framework by allowing the mapping from past values to the current value to follow an arbitrary or regime-switching nonlinear function. Major families include the Self-Exciting Threshold AR (SETAR), Smooth Transition AR (STAR), and neural network AR, each captu

econometrics

Nonlinear ARCH model

The Nonlinear ARCH (NARCH) model, introduced by Higgins and Bera (1992), extends Engle's original ARCH framework by allowing the power transformation of volatility to be estimated from the data rather than fixed at two. This flexibility captures a broader class of volatility dynamics observed in financial and macroecon

econometrics

Nonlinear ARDL

The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing the regressor into cumulative positive and negative partial sums, it tests whether increases and decreases in a variable exert different effects on the outcome — a f

econometrics

Nonlinear ARDL bounds test

The Nonlinear ARDL bounds test, developed by Shin, Yu, and Greenwood-Nimmo (2014), extends the linear ARDL framework to detect asymmetric long-run relationships in time series. By decomposing a regressor into positive and negative partial sums, NARDL simultaneously tests for cointegration and estimates separate long-ru

econometrics

Nonlinear Arellano-Bond GMM

Nonlinear Arellano-Bond GMM extends the classic Arellano-Bond difference-GMM framework to panel models where the conditional mean function is nonlinear in parameters or variables. It uses lagged levels of the dependent variable as instruments after first-differencing to remove individual fixed effects, yielding consist

econometrics

Nonlinear ARIMA model

The Nonlinear ARIMA model extends the classical Box-Jenkins ARIMA framework by allowing the conditional mean of a time series to depend on past values and past errors through a nonlinear function. It encompasses families such as Threshold AR (TAR/SETAR), Smooth Transition AR (STAR/LSTAR/ESTAR), and Markov-switching mod

econometrics

Nonlinear ARMA model

The Nonlinear ARMA (NARMA) model extends the classical linear ARMA framework by allowing the conditional mean to depend on past observations and past errors through an arbitrary nonlinear function. It captures complex dynamics — such as regime changes, asymmetric cycles, and threshold effects — that linear models miss,

econometrics

Nonlinear DCC-GARCH model

The Nonlinear DCC-GARCH model extends Engle's (2002) Dynamic Conditional Correlation framework by allowing correlations to respond asymmetrically to negative versus positive return shocks. Proposed by Cappiello, Engle, and Sheppard (2006), it is the standard tool for measuring time-varying co-movement and contagion eff

econometrics

Nonlinear difference GMM

Nonlinear Difference GMM extends the Arellano-Bond difference GMM estimator to models where the structural relationship between the outcome and its predictors is inherently nonlinear. By first-differencing to eliminate individual fixed effects and then applying GMM moment conditions with lagged levels as instruments, i

econometrics

Nonlinear Dynamic Panel Data Model

The nonlinear dynamic panel data model extends standard panel methods to settings where the outcome is binary, count-valued, or censored and where past realizations of the outcome directly affect current ones. It handles unobserved individual heterogeneity alongside state dependence, disentangling genuine persistence f

econometrics

Nonlinear EGARCH model

The Nonlinear EGARCH model extends Nelson's (1991) Exponential GARCH by allowing the news impact function to take a flexible nonlinear form, capturing asymmetric and nonlinear responses of conditional volatility to past shocks. It is widely used in financial econometrics to model leverage effects and complex volatility

econometrics

Nonlinear Engle-Granger Cointegration

Nonlinear Engle-Granger cointegration extends the classical two-step Engle-Granger procedure to detect long-run equilibria where adjustment toward the equilibrium is nonlinear — for example, faster above than below a threshold, or governed by a smooth transition mechanism. It is widely applied in financial economics, p

econometrics

Nonlinear Fixed Effects Model

The nonlinear fixed effects model extends fixed effects panel estimation to outcomes governed by nonlinear response functions — such as binary, count, or censored outcomes — while absorbing unobserved individual heterogeneity through unit-specific intercepts. Key special cases include conditional logit for binary outco

econometrics

Nonlinear GARCH model

The Nonlinear GARCH model extends the standard GARCH framework to capture asymmetric and nonlinear responses of conditional volatility to past shocks. It allows negative returns (bad news) to amplify volatility more than positive returns of equal magnitude, a phenomenon known as the leverage effect, which is empiricall

econometrics

Nonlinear GLS

Nonlinear Generalized Least Squares extends the classical GLS framework to regression models where the mean function is nonlinear in the parameters. It accounts for non-spherical errors — heteroscedasticity or autocorrelation — by pre-weighting the nonlinear objective with an estimated error covariance matrix, yielding

econometrics

Nonlinear Granger Causality

Nonlinear Granger causality extends the classic linear Granger causality framework to detect predictive relationships that operate through nonlinear dynamics. Using nonparametric or semi-parametric statistics based on correlation integrals or kernel density estimation, it identifies whether past values of one variable

econometrics

Nonlinear Hausman test

The Nonlinear Hausman test extends Hausman's (1978) endogeneity specification test to nonlinear models such as probit, logit, Tobit, and count-data regressions. It tests whether suspected regressors are endogenous — i.e., correlated with the error term — in a model where the outcome or the relationship is inherently no

econometrics

Nonlinear Johansen Cointegration

Nonlinear Johansen cointegration extends the classical Johansen framework to detect long-run equilibrium relationships among integrated time series when the adjustment process is nonlinear. Using rank-based transformations, the approach tests for cointegration without assuming a linear error-correction mechanism, makin

econometrics

Nonlinear KPSS Test

The nonlinear KPSS test extends the classic Kwiatkowski-Phillips-Schmidt-Shin stationarity test by modelling unknown smooth structural breaks in the deterministic trend using a Fourier approximation. Under the null hypothesis the series is stationary around a flexible nonlinear trend, guarding against spurious unit-roo

econometrics

Nonlinear MA model

The Nonlinear Moving Average (NMA) model extends the classical linear MA model by allowing the current observation to depend on past innovations through a nonlinear function rather than a simple weighted sum. It is used in time series analysis when error shocks transmit to outcomes in an asymmetric or state-dependent f

econometrics

Nonlinear NARDL

The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing an explanatory variable into its positive and negative partial sums, it tests whether increases and decreases in a regressor have different effects on the dependent

econometrics

Nonlinear OLS

Nonlinear Ordinary Least Squares (NLS) estimates regression models in which the conditional mean function is nonlinear in the parameters. Like standard OLS it minimises the sum of squared residuals, but because no closed-form solution exists the estimator is found by iterative numerical optimisation. Under standard reg

econometrics

Nonlinear Panel Data Analysis

Nonlinear panel data analysis applies nonlinear models — such as probit, logit, Poisson, or Tobit — to repeated observations on the same units over time. It accounts for unit-specific unobserved heterogeneity while capturing non-linear relationships between predictors and the outcome, making it essential when the depen

econometrics

Nonlinear PP unit root test

The Nonlinear Phillips-Perron unit root test extends the classic PP test by allowing the adjustment toward equilibrium to follow a nonlinear path — such as a smooth transition or threshold mechanism — rather than assuming a constant linear speed of adjustment. This makes it more powerful when the true data-generating p

econometrics

Nonlinear Random Effects Model

The nonlinear random effects model extends classical random effects estimation to settings where the outcome variable is binary, count-based, censored, or otherwise non-continuously distributed across panel units. It accounts for unobserved individual heterogeneity by treating unit-specific effects as random draws from

econometrics

Nonlinear SARIMA Model

The Nonlinear SARIMA model extends the classical Seasonal ARIMA framework by replacing the linear conditional mean function with a nonlinear specification — such as threshold switching or smooth transition — while retaining seasonal differencing and lag structure. It is used when seasonal time series exhibit regime-dep

econometrics

Nonlinear SVAR Model

The Nonlinear Structural VAR model extends the standard SVAR framework to allow structural relationships and dynamic responses to vary across economic regimes or states of the world. By imposing nonlinear transition mechanisms — such as threshold switching or smooth regime change — it captures asymmetric responses to s

econometrics

Nonlinear System GMM

Nonlinear System GMM extends the Generalized Method of Moments framework to estimate a system of structural equations in which the parameter vector enters the moment conditions nonlinearly. It jointly exploits moment restrictions across multiple equations, yielding efficiency gains over single-equation approaches when

econometrics

Nonlinear TGARCH model

The Nonlinear TGARCH (Threshold GARCH) model extends the standard GARCH framework by allowing positive and negative shocks of equal magnitude to exert different effects on future volatility. It models conditional volatility in terms of the absolute value of lagged residuals split by a sign threshold, capturing the well

econometrics

Nonlinear Toda-Yamamoto Causality

The Nonlinear Toda-Yamamoto causality test extends the classic Toda-Yamamoto (1995) modified Wald procedure to detect causal linkages that are hidden in the means of series but manifest through nonlinear dynamics such as asymmetries, threshold effects, or volatility transmission. It fits an augmented VAR on rank-transf

econometrics

Nonlinear VAR Model

The Nonlinear VAR (NLVAR) model extends the standard vector autoregression by allowing the dynamic relationships among multiple time series to switch or change smoothly depending on an observed threshold variable, a latent regime state, or a smooth transition function. It is used when economic systems exhibit asymmetri

econometrics

Nonlinear VECM

The Nonlinear VECM extends the standard linear VECM by allowing the speed of adjustment toward long-run equilibrium to differ depending on the sign, magnitude, or regime of deviations from that equilibrium. It captures asymmetric or threshold-driven dynamics in cointegrated time-series systems that a standard VECM woul

econometrics

Nonlinear WLS

Nonlinear Weighted Least Squares combines the flexibility of nonlinear regression with the variance-stabilizing power of observation-level weights. It minimises a weighted sum of squared residuals around a user-specified nonlinear mean function, making it the method of choice when the relationship is inherently nonline

econometrics

Nonlinear Zivot-Andrews test

The Nonlinear Zivot-Andrews test extends the classical Zivot-Andrews structural-break unit root test by embedding smooth-transition nonlinear adjustment into the test regression. It jointly searches for an endogenous structural break and allows the speed of mean-reversion to vary with distance from the attractor, produ

statistics

Nonparametric Quantile Regression

Quantile regression, introduced by Koenker and Bassett in 1978, models a chosen conditional quantile (such as the median or the 25th and 75th percentiles) of a continuous outcome rather than its mean. Its nonparametric variants fit these quantile relationships without assuming a distribution for the errors, making them

research statistics

Nonparametric Statistical Tests

Nonparametric (distribution-free) tests are statistical methods for hypothesis testing that do not assume data follow a specific probability distribution (e.g., normal), making them robust to departures from normality, outliers, and ordinal data. The Mann-Whitney U test (1947) and Kruskal-Wallis test (1952) extend hypo

research statistics

Null Hypothesis Testing

Null Hypothesis Significance Testing (NHST) is the dominant statistical framework in empirical research. The null hypothesis (H₀) represents the default assumption—typically 'no effect' or 'no difference'—while the alternative hypothesis (H₁) represents the claim being tested. The test calculates the probability of obs

econometrics

OLS Regression

Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).

statistics

One-way ANOVA

One-way ANOVA is a parametric hypothesis test that compares the means of three or more independent groups on a single continuous outcome to decide whether at least one group mean differs. It rests on the variance-partitioning framework introduced by Ronald A. Fisher in 1925.

machine learning

Online Bagging

Online Bagging is a streaming ensemble method introduced by Oza and Russell in 2001 that adapts the classical bootstrap aggregating (Bagging) framework to the online learning setting. Instead of resampling a fixed dataset, each incoming instance is fed to every base learner a Poisson(1)-distributed number of times, fai

machine learning

Online Logistic Regression

Online Logistic Regression fits a logistic classifier one sample (or mini-batch) at a time via stochastic gradient descent, updating model weights as each observation arrives rather than waiting to see the full dataset. This makes it the standard choice for high-volume, streaming, or memory-constrained binary classific

econometrics

Ordered Logit

Ordered logit is a cumulative regression model for an ordinal dependent variable, fitting a logit (or probit) link to the cumulative category probabilities. Developed in McCullagh's 1980 treatment of regression models for ordinal data, it is the standard tool for Likert-scale, rating, and ranked outcomes.

psychometrics

Ordinal CFA

Ordinal confirmatory factor analysis (Ordinal CFA) tests a pre-specified factor structure when the observed indicators are ordinal — typically Likert-type survey items. By using polychoric correlations and robust estimators such as WLSMV, it avoids the bias that arises from treating categorical responses as continuous.

psychometrics

Ordinal Cronbach's Alpha

Ordinal Cronbach's alpha is a reliability coefficient computed from polychoric or polyserial correlations rather than Pearson correlations, making it appropriate for Likert-type and other ordinal item response data. It corrects the systematic downward bias that standard Cronbach's alpha produces when items are treated

psychometrics

Ordinal EFA

Ordinal exploratory factor analysis discovers latent factors underlying a set of ordinal items — typically Likert scales — by computing polychoric correlations among the items and then applying a weighted least squares estimator. It avoids the distortions that arise when continuous EFA methods are naively applied to or

statistics

Ordinal Logistic Regression

Ordinal logistic regression — most commonly the proportional-odds model — estimates the relationship between one or more predictors and an ordered categorical outcome (e.g., Likert scales, disease severity grades, educational attainment levels). It models cumulative log-odds across the ordered categories while assuming

statistics

Ordinal Regression

Ordinal logistic regression models an ordered categorical outcome — such as a Likert rating, a satisfaction level, or an education tier — as a function of predictors. It is the ordinal extension of logistic regression, developed in standard treatments such as Agresti's Analysis of Ordinal Categorical Data (2010), and i

spatial analysis

Ordinary Kriging

Ordinary Kriging (OK) is the standard geostatistical method for interpolating a continuous spatial variable at unsampled locations. It derives optimal, unbiased weights from the spatial covariance structure of the data, making it the Best Linear Unbiased Predictor (BLUP) under stationarity assumptions. Unlike simpler d